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arXiv:2511.21220

Nucleation and wetting transitions in three-component Bose-Einstein condensates in Gross-Pitaevskii theory: exact results

Jonas Berx, Nguyen Van Thu, Joseph O. Indekeu

cond-mat.quant-gascond-mat.stat-mechquant-phSubmitted Nov 26, 2025• Announced Nov 27, 2025• 0 citations
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Abstract

Nucleation and wetting transitions are studied in a three-component Bose-Einstein condensate mixture within Gross-Pitaevskii theory. For special cases of intermediate segregation between components 1 and 2, the nucleation phase transition of a surfactant film of component 3 is obtained by exact solution. Additional exact results for the nucleation transition are derived in the limit of strong segregation between components 1 and 2. In this limit the exact first-order wetting phase boundary is obtained using analytical and numerical methods, and is contrasted with the exact nucleation and wetting phase boundary derived previously for a two-component Bose-Einstein condensate mixture at a hard optical wall. Exact results for the three-component mixture are compared with results from the double-parabola approximation used in an earlier work.

Comments
24 pages, 9 figures

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Nucleation and wetting transitions are studied in a three-component Bose-Einstein condensate mixture within Gross-Pitaevskii theory. For special cases of intermediate segregation between components 1 and 2, the nucleation phase transition of a surfactant film of component 3 is obtained by exact solution. Additional exact results for the nucleation transition are derived in the limit of strong segregation between components 1 and 2. In this limit the exact first-order wetting phase boundary is obtained using analytical and numerical methods, and is contrasted with the exact nucleation and wetting phase boundary derived previously for a two-component Bose-Einstein condensate mixture at a hard optical wall. Exact results for the three-component mixture are compared with results from the double-parabola approximation used in an earlier work.
In previous work within Gross-Pitaevskii (GP) theory for ultracold gases, wetting phase transitions were predicted for a phase-segregated two-component Bose-Einstein condensate (BEC) adsorbed at an optical wall. The wetting phase diagram was found to depend on intrinsic atomic parameters, being the masses and the scattering lengths, and on the extrinsic wall boundary condition. Here we study wetting transitions in GP theory without an optical wall in a setting with three phase-segregated BEC components instead of two. The boundary condition is removed by replacing the wall with the third component and treating the three phases on an equal footing. This leads to an unequivocal wetting phase diagram that depends only on intrinsic atomic parameters. It features first-order and critical wetting transitions, and prewetting phenomena. The phase boundaries are computed by numerical solution of the GP equations. In addition, useful analytic results are obtained by extending the established double-parabola approximation to three components.
By means of Gross-Pitaevskii theory we investigate the possibility of wetting phase transition in three-component Bose-Einstein condensates within the strong segregation between components 1 and 2. Third component plays the role of a surfactant, which can wet the interface formed by components 1 and 2. The case of symmetry of components 1 and 2, the equation for nucleation line and wetting phase diagram are studied. By linearizing the set of three-coupled Gross-Pitaevskii equations, the wave functions of the components are found. An analytical approximation for the surfactant thickness in the prewetting phase is presented. The results indicate that the surfactant thickness in the prewtting phase varies linearly with the chemical potential ratio in the logarithmic scale.
Within the framework of Gross-Pitaevskii theory, we investigate the effects of intraspecies interactions on the nucleation transition and the wetting phase diagram of dilute ternary Bose-Einstein condensate in the regime of strong segregation between two components. The analyses are carried out using both the analytical double-parabola approximation (DPA) and numerical computations. Our results show that the DPA provides a reliable approximation for describing the nucleation transition. For the wetting phase diagram, we find that the DPA is in excellent agreement with numerical results in symmetric systems, particularly in the completely symmetric case, whereas it fails to provide an adequate description for asymmetric systems.
Abstract The interfacial phenomena in multicomponent Bose-Einstein condensates include a rich variety of wetting transitions. Previous studies of a wall-less, three-component system have primarily fo-cused on the continuous (critical) wetting transition, leaving the phase diagram incomplete. In this work, we present a complete theoretical description of this system at zero temperature based on the Gross-Pitaevskii theory and a semi-analytical double-parabola approximation. We derive the analytical conditions for both discontinuous (first-order) and continuous (critical) wetting transitions by calculating the grand potential and the associated interfacial tensions. Synthesizing these results, we construct the complete wetting phase diagram and, crucially, identify the tricritical point where the first-order and critical transition lines meet. This complete phase diagram provides a quantitative roadmap for future experiments exploring complex interfacial phenomena in quantum fluids.
We identify the adsorbed index as an experimentally accessible order parameter for the wetting phase transition in dilute ternary Bose–Einstein condensates (BECs). By tracking the nucleation and growth of a surfactant film of the third component at the interface between two immiscible condensates, we show that the adsorbed index exhibits a logarithmic divergence with the chemical-potential ratio in the prewetting phase. Numerical Gross–Pitaevskii calculations are consistent with analytical predictions from the double-parabola approximation, confirming the reliability of the approach. Unlike the conventional surfactant layer thickness, which becomes ill-defined near the nucleation point, the adsorbed index remains well defined throughout the entire prewetting-wetting regime and is directly proportional to the number of condensed atoms in the surfactant component, a quantity that is readily measurable in ultracold-atom experiments and tunable via Feshbach resonances. Our results offer a realistic opportunity to observe wetting transitions in multicomponent quantum gases.
An ultralow-temperature binary mixture of Bose-Einstein condensates adsorbed at an optical wall can undergo a wetting phase transition in which one of the species excludes the other from contact with the wall. Interestingly, while hard-wall boundary conditions entail the wetting transition to be of first order, using Gross-Pitaevskii theory we show that first-order wetting as well as critical wetting can occur when a realistic exponential optical wall potential (evanescent wave) with a finite turn-on length $\ensuremath{\lambda}$ is assumed. The relevant surface excess energies are computed in an expansion in $\ensuremath{\lambda}/{\ensuremath{\xi}}_{i}$, where ${\ensuremath{\xi}}_{i}$ is the healing length of condensate iii. Experimentally, the wetting transition may best be approached by varying the interspecies scattering length a12{a}_{12}a12​ using Feshbach resonances. In the hard-wall limit, $\ensuremath{\lambda}\ensuremath{\rightarrow}0$, exact results are derived for the prewetting and first-order wetting phase boundaries.